Deformation of Lie algebras and Lie algebras of deformations
Harald Bjar, Olav Arnfinn Laudal (1990)
Compositio Mathematica
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Harald Bjar, Olav Arnfinn Laudal (1990)
Compositio Mathematica
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Dietrich Burde (2006)
Open Mathematics
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In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields...
Hernández, I., Peniche, R. (2008)
International Journal of Mathematics and Mathematical Sciences
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Adrian Vasiu (2005)
Open Mathematics
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We include short and elementary proofs of two theorems that characterize reductive group schemes over a discrete valuation ring, in a slightly more general context.
Kenny De Commer (2015)
Banach Center Publications
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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...
de Graaf, W.A. (2005)
Experimental Mathematics
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Francesco Catino, Ernesto Spinelli (2007)
Bollettino dell'Unione Matematica Italiana
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For a group algebra KG of a non-abelian group G over a field K of positive characteristic p we study the strong Lie derived length of the associated Lie algebra.
Richter, David A. (1999)
Journal of Lie Theory
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Cohen, A.M., de Graaf, W.A., Rónyai, L. (1997)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Ian Stewart (1973)
Compositio Mathematica
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